By Kato's result [1]}, i.e., Schrödinger operator \(H = -\Delta + p(x)\)  has no positive eigenvalue with an \(L^2\) -eigenfunction if \(p(x) = o(|x|^{-1})\) , then (REF ) has no solution. We show that (REF )-(REF ) has no non-trivial radial solution for \(p >\frac{8}{3}\)  and \(\alpha _i<0(i=1,2)\) .
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